Consider the events C 1 , C 2 , C 3 (a) Suppose C 1 , C 2 , C 3 are mutually exclusive events If P(C i ) p i , i 1, 2, 3, what is the restriction on the sum p 1 p 2 p 3 (b) In the notation of part (a), if p 1 4 10, p 2 3 10, and p 3 5 10, are C 1 , C 2 , C 3 mutually exclusive For the last two exercises it is assumed that the reader is familiar with fields

Question: Consider the events C 1 , C 2 , C 3 . (a) Suppose C 1 , C 2 , C 3 are mutually exclusive

Consider the events C₁, C₂, C₃.
(a) Suppose C₁, C₂, C₃ are mutually exclusive events. If P(C_i) = p_i, i = 1, 2, 3, what is the restriction on the sum p₁ + p₂ + p₃?
(b) In the notation of part (a), if p₁ = 4/10, p₂ = 3/10, and p₃ = 5/10, are C₁, C₂, C₃ mutually exclusive?
For the last two exercises it is assumed that the reader is familiar with σ-fields.

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